This project consists of an experiment regarding the creation of graphs describing bidirectional relations between data features in order to lay the groundwork for a homogeneous prediction environment where all data is treated equally.
Machine learning is all about making inferences and predictions on new data. The training features are usually isolated from the output results.
In a supervised learning scenario, creating a model which would predict Y by using X requires the collection of data points which contain both input and output data. Those data points are used to create a directed relation between X and Y. In order to reverse the problem, the model has to be restructured and retrained, having only one purpose at a time. Additionally, the model is blind to valuable insights regarding correlations between elements from X alone and elements from Y alone. Classical machine learning models discriminate data by treating data features differently at a high level. It narrows the model to a specific problem, despite the possibilities of a homogenous data connectome.
The Iris Dataset data set consists of 50 samples from each of three species of Iris. Four features were measured from each sample: the length and the width of the sepals and petals, in centimetres.
A classical approach is to specificy a task, e.g. predict the petal width from the other features. A machine learning model, like a multilayer perceptron would be trained on the (X -> Y) pairs. Alternatively, information describing the sepal width from the petal width would not be harnessed (Y -> X). Neither would the information describing the sepal width from the sepal length (X -> X).
At first, a complete graph is created with a node for each feature (4 in our case). Then, a linear regression is trained between every two nodes (for a total of 12 in our Iris case).
After training, we have obtained the following values for slopes and intercepts.
(0, 1) [-0.05726823] [0.42088597]
(0, 2) [1.85750967] [-0.89867058]
(0, 3) [0.75384088] [-0.41421703]
(1, 0) [-0.20887029] [0.81542772]
(1, 2) [-1.71120139] [1.11712251]
(1, 3) [-0.62754618] [0.3785177]
(2, 0) [0.4091259] [0.54442026]
(2, 1) [-0.10333897] [0.42719011]
(2, 3) [0.41641913] [-0.05447079]
(3, 0) [0.88751905] [0.61131356]
(3, 1) [-0.20257264] [0.40725126]
(3, 2) [2.22588531] [0.15553342]
In this experiment we compare the cost of the average of the 3 regression results toward one node (we iterate between all 4 and repeat the tests) to the individual results.
Cost: 0.0
Cost: 1.7749370367472766e-28
Cost: 1.0366125332669858e-29
Cost: 3.520415049065206e-28
Special cost: 1.601880675664417e-28
Cost: 1.1093356479670479e-29
Cost: 0.0
Cost: 4.930380657631324e-30
Cost: 4.686943112660777e-30
Special cost: 6.039716305598372e-31
Cost: 7.888609052210118e-29
Cost: 2.0194839173657902e-28
Cost: 0.0
Cost: 1.2823920090499073e-28
Special cost: 1.262177448353619e-29
Cost: 7.888609052210118e-29
Cost: 2.8398992587956425e-29
Cost: 2.2790684589900794e-29
Cost: 0.0
Special cost: 3.865418435582958e-29
We can notice that there is a 0 cost from a node to itself. More importantly, the average regression (Special cost) performance is, effectively, above average, being the best in half the cases.